Cesàro Means of Subsequences of Double Sequences - Taş, Emre; Orhan, Cihan (Sarajevo Journal of Mathematics, 2020)
In this paper we characterize the convergence and $\left( C,1,1\right) $ summability of a double sequence. In particular we study conditions under which the convergence or $\left( C,1,1\right) $ summability of a double sequence carry over to that of its subsequences, \ and conversely, whether these properties for suitable subsequences imply them for the sequence itself. We show, for instance, that a bounded double sequence is $\left(C,1,1\right) $ summable if and only if almost all of its subsequences are $\left( C,1,1\right) $ summable.